How can I make this Dodecahedron shaped product?
As @Robin Betts said, Use the addon Add Mesh: Extra Objects to create the Dodecahedron.

Then in edit mode select the rouge edges that you can't use and dissolve them.

The select everything and delete only faces.
Back in object mode and convert to curve.
Now it is a curve object you can easily add roundness to the segments by increasing the bevel size, this is nice because you can come back later to change the size if you need to.

Now it's a simple matter of adding your favorite sphere shape and snapping its centre to every vertex of the dodecahedron. I recommend using ALT-D to duplicate so that if you want to change their size you can do them all at the same time.

For the seams, you could add a plane along where it needs to be, then use the knife tool to cut it up with some randomness and give it some slight thickness with a Solidify modifier and maybe a subsurf if it needs it.